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Monopoles, three-algebras and ABJM theories with \( \mathcal{N} = 5,6,8 \) supersymmetry

  • Andreas Gustavsson
Article

Abstract

We extend the hermitian three-algebra formulation of ABJM theory to include U(1) factors. With attention payed to extra U(1) factors, we refine the classification of \( \mathcal{N} = 6 \) ABJM theories. We argue that essentially the only allowed gauge groups are SU(N) × SU(N), U(N) × U(M) and Sp(N) × U(1) and that we have only one independent Chern-Simons level in all these cases. Our argument is based on integrality of the U(1) Chern-Simons levels and supersymmetry. A relation between monopole operators and Wilson lines in Chern-Simons theory suggests certain gauge representations of the monopole operators. From this we classify cases where we can not expect enhanced \( \mathcal{N} = 8 \) supersymmetry. We also show that there are two equivalent formulations of \( \mathcal{N} = 5 \) ABJM theories, based on hermitian three-algebra and quaternionic three-algebra respectively. We suggest properties of monopoles in \( \mathcal{N} = 5 \) theories and show how these monopoles may enhance supersymmetry from \( \mathcal{N} = 5 \) to \( \mathcal{N} = 6 \).

Keywords

Field Theories in Lower Dimensions Extended Supersymmetry Chern-Simons Theories M-Theory 

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Copyright information

© SISSA, Trieste, Italy 2011

Authors and Affiliations

  1. 1.Center for quantum spacetime (CQUeST)Sogang UniversitySeoulKorea
  2. 2.School of Physics & AstronomySeoul National UniversitySeoulKorea

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